The present invention relates to an interferometer and method and more particularly to a method and apparatus for performing phase shifting interferometry and data reduction.
Phase shifting interferometry (PSI) is known in the art and involves acquiring a sequence of interferograms, where between interferograms, the phase of one incident beam of the interferometer has been shifted by some fraction of a wavelength relative to another incident beam. Well-known advantages of the PSI include (1) high measurement accuracy, (2) rapid measurement, (3) good results even with low contrast fringes, (4) results independent of intensity variations across the pupil, and (5) phase obtained at a fixed grid of data points. In PSI the phase difference between the two interfering beams is varied in a known manner, and measurements are made of the intensity distribution of the interfering beams. The technique of phase shifting may be accomplished by several different approaches, including, the use of a rotating waveplate, a piezoelectric transducer driven mirror, moving gratings, acoustooptic modulators or Zeeman split lasers. These phase shifting techniques require precisely calibrated, sophisticated opto-mechanical devices and control systems so that the phase shifts between interferograms are either known or constant.
Several algorithms are known which use the intensities of the various interferograms at each point to solve for the phase at that point. With conventional algorithms and techniques, the size of the phase shift must either be known, or it must be known that all of the phase shifts are exactly the same. While there are many interferometry techniques that utilize phase shifting, each consists of solving a set of linear equations at each pixel of the interferogram. The set of equations is generated by acquiring an interferogram for each equation, with a known or constant phase shift, .DELTA., between successive interferograms.
The basic equation for interferometry is: EQU I.sub.(i,j) =I.sub.A(i,j) +I.sub.B(i,j) +2[I.sub.A(i,j) I.sub.B(i,j,) ].sup.1/2 cos[.PHI..sub.(i,j)] (1)
where i and j define pixel locations on the image plane, I.sub.A and I.sub.B are the intensities of the reference and object beams at pixel location (i,j), and .PHI. is the relative optical phase of the two beams at that location. Phase .PHI. is the final data desired in all interferometric experiments. It is the phase which is used to calculate related physical parameters such as density, pressure, temperature, and displacement.
The complete set of equations for k-1 phase shifts (k interferograms) is: ##EQU1## where .DELTA..sub.k is the phase shift for interferogram k.
One can then solve this set of equations at each point of the interferogram for I.sub.A, I.sub.B and .PHI. with 3 equations, given a known phase shift, or with four equations if the phase shift is unknown, but constant. Various algorithms are known which permit further statistical certainty by using more phase shifted interferograms. If the phase shift varies in an unknown manner, each additional interferogram simply generates one more equation and one more unknown. One must usually also assume that the independent incident beam intensities are constant throughout this process of data acquisition.
In the typical two-beam interferogram, the beams which interfere contain various types of non-uniformities which are either constant or varying in time. Constant intensity variations are represented by the Gaussian intensity profile of ideal laser beams, or perhaps by deviation from the ideal caused by dust and imperfections in or on the optical components which form the beams. These might be referred to as "fixed pattern noise". Time varying intensity patterns, on the other hand, might be due to variations in laser power, dust particles moving through the beams, variations in the index of refraction of the air through which the beam moves, or various statistical noise sources in the laser or recording media. These noise sources are generally controlled by time averaging, where the interferogram is recorded over an extended time period, during which, the time varying effects may be averaged out. In order to minimize the effects of these non-uniformities in the interfering beams, and thereby enhance the data quality, elaborate and precise optical configurations are required. These elaborate optical configurations are expensive and require experienced operators performing under very meticulously controlled conditions.
It is an object of this invention to provide a noise reduction method which simplifies interferometric data reduction.
It is another object of this invention to provide a beam shuttered phase shifting interferometry method to facilitate the technique of phase shifting interferometry.
It is a further object of this invention to provide a phase shifting interferometer which facilitates interferometry data reduction and requires minimum operator intervention.
It is still a further object of this invention to provide a novel apparatus for performing phase shifting interferometry that does not require expensive and sophisticated hardware for controlling the phase shifting process.
Additional objects, advantages and novel features of the invention will become apparent to those skilled in the art upon examination of the following and by practice of the invention.